pure substance_steam tables
TRANSCRIPT
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Dr. Mandar M. Lele
Pure Substance is one with uniform and invariant chemical composition.
Eg: Elements and chemical compounds are pure
substances. (water, stainless steel)
Mixtures are not pure substances. (eg: Humid
air)
Pure Substance
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Dr. Mandar M. Lele
Exception!! Air is treated as a pure substance
though it is a mixture of gases.
In a majority of cases a minimum of two
properties are required to define the state of a
system. The best choice is an extensive property
and an intensive property
Pure Substance
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Dr. Mandar M. Lele
Gibbs Phase Rule determines what is expected to define
the state of a system
F=C+2-P
F= Number of degrees of freedom (i.e.., no. of properties required)
C= Number of components P= Number of phases
E.g.: Nitrogen gas C=1; P=1. Therefore, F=2
Properties of Substance
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Dr. Mandar M. Lele
To determine the state of the nitrogen gas in a cylinder two
properties are adequate.
A closed vessel containing water and steam in equilibrium:
P=2, C=1
Therefore, F=1. If any one property is specified it is sufficient.
A vessel containing water, ice and steam in equilibrium
P=3, C=1 therefore F=0. The triple point is uniquely defined.
Properties of Substance
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Dr. Mandar M. Lele
The most common liquid is water. It has peculiar
properties compared to other liquids.
Solid phase is less dense than the liquid phase (ice floats on water)
Water expands on cooling ( a fully closed vessel
filled with water will burst if it is cooled below the freezing point).
The largest density of water near atmospheric
pressure is at 4°c.
Properties of Liquids
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Dr. Mandar M. Lele
The zone between the saturated liquid and the
saturated vapour region is called the two
phase region - where the liquid and vapour
can co-exist in equilibrium.
Properties of Liquids
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Quality or Dryness FractionIf in 1kg of liquid-vapour mixture, x kg is the mass of vapour and (1- x) kg of mass of liquid, then x is known as the quality or dryness fraction of the liquid-vapour mixture. Therefore, quality indicates the mass fraction of vapour in a liquid vapour mixture , or v
v l
mxm m
=+
Where, mv = mass of vapour
ml = mass of liquid
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Dr. Mandar M. Lele
The value of x varies between 0 and 1. For
saturated water when water just starts
boiling, x = 0, and for saturated vapour,
when vaporization is complete, x = 1, for
which the vapour is said to be dry saturated.
Quality or Dryness Fraction
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Dr. Mandar M. Lele
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It is the highest temperature at which the liquid and
vapour phases can coexist.
At the critical point hfg ,ufg and vfg are zero.
Liquid vapour meniscus will disappear.
Specific heat at constant pressure is infinite.
A majority of engineering applications (eg: steam based power generation; Refrigeration, gas liquefaction) involve thermodynamic processes close to saturation.
Characteristics of the critical point
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Dr. Mandar M. Lele
Characteristics of the critical pointThe simplest form of vapour pressure curve is
ln p= A+B/T valid only near the triple point.(Called
Antoine’s equation)
The general form of empirical vapour pressure curve is ln p=ln pc+ [A1(1-T/Tc) + A2(1-T/Tc)1.5+ A3(1-T/Tc)2+……]/(T/Tc) (Called the Wagner’s equation)
Definitions: Reduced pressure pr =p/pc;
Reduced temperature Tr =T/Tc
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Dr. Mandar M. Lele
Characteristics of the critical pointFor saturated phase often its enthalpy is an important property.
Enthalpy-pressure charts are used for refrigeration cycle analysis.
Enthalpy-entropy charts for water are used for steam cycle
analysis.
Note: Unlike pressure, volume and temperature which have
specified numbers associated with it, in the case of internal
energy, enthalpy (and entropy) only changes are required.
Consequently, a base (or datum) is defined - as you have seen in the case of water.
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Dr. Mandar M. Lele
Let V be total volume of liquid vapour mixture of quality x, Vf the volume of saturated liquid and Vg the volume of saturated vapour, the corresponding masses being m, mf and mg respectively.
Now, m = mf + mg
V = Vf + Vg
So, m v = mf vf + mg vg
= (m –mg) vf + mg vg
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Dr. Mandar M. Lele
1
(1 )
,
g gf g
f g
g
g
f
m mv v v
m mv x v x v
mwhere x
mv specific volume of saturated vapour
v specific volume of saturated liquid
v specific volume of mixtureof quality x
⎡ ⎤= − +⎢ ⎥⎣ ⎦
= − +
=
=
=
=
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Dr. Mandar M. Lele
gf
gf
gf
uxuxu
hxhxh
sxsxsSimilarly
+−=
+−=
+−=
)1(
)1(
)1(
Where s, h, u refer to the mixture of quality x. the suffix f and g indicates the conditions of -Saturated liquid and saturated vapour respectively
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Dr. Mandar M. Lele
(1 )
( )
,
f g
f g f
f fg
f fg
f fg
f fg
v x v x v
v v x v v
v v x v
Similarlyh h x h
s s x s
u u xu
= − +
= + −
= +
= +
= +
= +
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Dr. Mandar M. Lele
,
,
( )
(1 )
f fg
g
g f
f f g g f g g g
f g
However x
Volume fractionof vapour or voidagevv
m m m
v v v v v v
ρ ρ ρ
α
ρ ρ ρ ρ ρ
ρ α ρ α ρ
≠ +
=
= +
= + = − +
= − +
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Dr. Mandar M. Lele
Steam TablesThe properties of water are arranged in the steam tables as function of pressure and temperature. Separate tables are provided to give the properties of water in the saturation states and in the liquid vapour phases.
The internal energy of saturated water at the triple point (t = 0.01 0C) is arbitrarily chosen zero.
Since h = u + pv, enthalpy of saturated water at 0.01 0C is slightly positive because of the small value of (pv) term.
The entropy of saturated water is also chosen to be zero at the triple point
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Dr. Mandar M. Lele
Saturation StatesWhen a liquid and its vapour are in equilibrium at certain When a liquid and its vapour are in equilibrium at certain pressure and temperature, only the pressure or the temperature ipressure and temperature, only the pressure or the temperature is s sufficient to identify the saturation state.sufficient to identify the saturation state.
If pressure is given, the temperature of the mixture gets fixed,If pressure is given, the temperature of the mixture gets fixed,which is known as saturation temperature, or if the temperature which is known as saturation temperature, or if the temperature is given, the saturation pressure gets fixed. is given, the saturation pressure gets fixed.
Saturation liquid or saturated vapour has only on independent Saturation liquid or saturated vapour has only on independent variable, i.e. only one property is required to b known to fix uvariable, i.e. only one property is required to b known to fix up p the state.the state.
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Dr. Mandar M. Lele
Liquid – Vapour Mixture
Let us consider a mixture of saturated liquid water and water vapour in equilibrium at pressure p and temperature t. The composition of the mixture by mass will be given by its quality x
fgf
fgf
fgf
fgf
sxss
hxhh
uxuu
vxvv
+=
+=
+=
+=
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Dr. Mandar M. Lele
Superheated Vapour
When the temperature of vapour is greater than the
saturation temperature corresponding to given pressure,
the vapour is said to be superheated.
The difference between the temperature of superheated
vapour and saturated temperature at that pressure is
called the superheat or degree of superheat i.e. (tsup-tsat)
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Dr. Mandar M. Lele
Compressed Liquid
When the temperature of liquid is less than the saturation temperature corresponding to given pressure, the liquid is called compressed liquid.
The properties of liquid vary little with pressure- so the properties are taken from the saturation tables at the temperature of compressed liquid
The difference between the temperature of subcooled liquid and saturated temperature at that pressure is called as subcooling or degree of subcoolingi.e. (tsat-tsub)
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Charts for Thermodynamic
Properties
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Superheating and Subcooling T-s chart
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Dr. Mandar M. Lele
The presentation of properties of substances in the form of a chart has certain obvious advantages. The manner of variation of properties is clearly demonstrated in the chart and there is no problem of interpolation.
T-s chart – its scale is small and limited in use.
h-s plot or Mollier chart has a larger scale to provide data suitable for many computations
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Dr. Mandar M. Lele
The state of a pure substance gets fixed if two independent properties are given. A pure substance is thus said to have two degrees of freedom. Of all thermodynamic properties, it is easiest to measure the pressure and temperature of a substance. Therefore, whenever pressure and temperature are independent properties, it is the practice to measure them to determine that state of the substance.
Measurement of Steam Quality
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Dr. Mandar M. Lele
This is done in the compressed liquid region or the superheated vapour region where the measured values of pressure and temperature would fix up the state. But when the substance is in the saturation state or two-phase region the measured values of pressure and temperature could apply equally well to saturated liquid point f, saturated vapour point g, or to mixtures of any quality, points x1, x2, x3 Of the two properties, p and t, only one is independent; the other is a dependent property.
Measurement of Steam Quality
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Dr. Mandar M. Lele
If pressure is given, the saturation temperature gets automatically fixed for the substance, In order to fix up the state of the mixture, apart from either pressure or temperature, one more property, such as specific volume, enthalpy or composition of the mixture (quality) is required to be known.
Since it is relatively difficult to measure the specific volume of a mixture, devices such as calorimeters are used for determining the quality or the enthalpy of the mixture.
Measurement of Steam Quality
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Dr. Mandar M. Lele
Measurement of Steam Quality
In the measurement of quality, the object is always
to bring the state of the substance from the two-
phase region to the single-phase or superheated
region, , where both pressure and temperature are
independent, and measured to fix the state, either by
adiabatic throttling or electric heating.
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Dr. Mandar M. Lele
Types of Calorimeters used for measurement of Steam Quality
• Barrel Calorimeter
• Separating Calorimeter
• Throttling Calorimeter
• Combined Separating and Throttling calorimeter
• Electrical Calorimeter
Measurement of Steam Quality
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Dr. Mandar M. Lele
Dryness fraction of steam can be found out very conveniently by barrel calorimeter as shown in figure. A vessel contains a measured quantity of water. Also water equivalent of the vessel is determined experimentally and stamped platform of weighing machine. Sample of steam is passed through the sampling tube into fine exit holes for discharge of steam in the cold water.
Barrel Calorimeter
The steam gets condensed and the temperature of water rises. The weighing machine gives the steam condensed.
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Dr. Mandar M. Lele
where, x = quantity of steam in the main pipe hfg = latent heat of vaporization at pressure p Cp = specific heat of water at constant pressure p m = mass of steam condensedM =Equivalent mass of water at commencementtS =Sat. temperature; t1 = temperature of Water at commencementt2 = final temperature after steam has condensed
From the law of conservation of energy,
2 2 1
2 1 2
{ ( )} ( )
{ ( ) ( )}fg s p
p s
fg
HeatLost HeatGainm x h t t C M t t
C M m t t t tx
h
=+ − = −
− − −=
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Dr. Mandar M. Lele
The wet steam enters at the top from the main steam pipe through holes in the sampling pipe facing up stream which should be as far as possible downstream from elbows and valves to ensure representative sample of steam when in operation the wet steam entering passes down the central passage and undergoes a sudden reversal of direction of motion when strikes perforated cup.
The condensate thus collected in collector tank and dry steam moves upwards to condenser
Separating Calorimeter
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Dr. Mandar M. Lele
Separating Calorimeter
Advantages:
Quick determination of dryness fraction of very wet steam
Disadvantages:
It leads to inaccuracy due to incomplete separation of water
Dryness fraction calculated is always greater than actualv
v l
mxm m
=+
Where, mv = mass of steam read from gauge of condenser and weighed
ml = mass of water separated in specific time interval
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Dr. Mandar M. Lele
In the throttling calorimeter, a sample of wet steam of mass m and at pressure P1 is taken from the steam main through a perforated sampling tube .Then it is throttled by the partially-opened valve (or orifice) to a pressure P2measured by mercury manometer, and temperature t2, so that after throttling the steam is in the superheated region
Throttling Calorimeter
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Dr. Mandar M. Lele
The process is shown on the T-s and h-s
Throttling Calorimeter
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Dr. Mandar M. Lele
The steady flow energy equation gives the enthalpy after throttling as equal to enthalpy before throttling. The initial and final equilibrium states 1 and 2 are joined by a dotted linesince throttling is irreversible (adiabatic but not isentropic) and the intermediate states are non-equilibrium states not describable by thermodynamic coordinates. The initial state (wet) is given by P1and x1 and the final state by P2 and t2 (superheated).
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Dr. Mandar M. Lele
Now
1
1
11
21
21
21
p
p
pp
fg
f
fgf
h
hhx
or
hhxhhh
−=
=+=
With P2 and t2 being known, h2 can be found out from the superheated steam table. The values of hf and hfg are taken from the saturated steam table corresponding to pressure P1. Therefore, the quality of the wet steam x1 can be calculated.
Throttling Calorimeter
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Dr. Mandar M. Lele
For example, if P2 = 1 atm., then t2 = 105°C and the state 2 after throttling gets fixed as shown in above Fig.. From state 2, the constant enthalpy line intersects the constant pressure P1 line at 1. Therefore, the quality x1 is the minimum quality that can be measured simply by throttling. If the quality is, say, x1’than x1 then after throttling to P2 = 1 atm., the superheat after throttling is less than 5°C. If the quality is x1’’ then throttling to 1atm. does not give any superheat at all..
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Dr. Mandar M. Lele
To be sure that steam after throttling is in the single-phase or superheated region, a minimum of 5°C superheat is desired. So ifthe pressure after throttling is given and the minimum 5°C superheat is prescribed, then there is the minimum quality of steam (or the maximum moisture content) at the given pressure P1 which can be measured by the throttling calorimeter.
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Dr. Mandar M. Lele
Throttling Calorimeter
Advantages:
Dryness fraction of very dry
steam can be found out easily
Disadvantages:
It is not possible to find dryness
fraction of very wet steam
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Dr. Mandar M. Lele
When the steam is very wet and the pressure after throttling is not low enough to take the steam to the superheated region, then a combined separating and throttling calorimeteris used for the measurement of quality.
Combined Separating and Throttling calorimeter
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Dr. Mandar M. Lele
Steam from the main is first passed through a separator where some part of the moisture separates out due to the sudden changein direction and falls by gravity, and the partially dry vapour is then throttled and taken to the superheated region.
Combined Separating and Throttling calorimeter
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Dr. Mandar M. Lele
In Fig. process 1-2 represents the moisture separation from the wet sample of steam at constant pressure P1 and process 2-3 represents throttling to pressure P2. With P2 and t3 being measured, h3 can be found out from the superheated steam table.Now
11 223 pp fgf hxhhh +==Therefore x2, the quality of steam after partial moisture separation can be evaluated
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Dr. Mandar M. Lele
If m kg of steam, is taken through the sampling tube in t s, m1 kg of it is separated, and m2 kg is throttled and then condensed to water and collected, then m = m1 + m2 and at state 2, the mass of dry vapour will be x2 m2. Therefore, the quality of the sample of steam at state l, x1 is given by . .
Combined Separating and Throttling calorimeter
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Dr. Mandar M. Lele
21
22
1 11
mmmx
stateatmixturevapourliquidofmassstatevapourdryofmassx
+=
−=
Combined Separating and Throttling calorimeter
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Dr. Mandar M. Lele
Electrical Calorimeter
The quality of wet steam can also be measured by an electric Calorimeter. The sample of steam is passed in steady flow through an electric heater, as shown. The electrical energy input Q should be sufficient to take the steam to the superheated region where pressure P2 and temperature t2 are measured. If I is the current flowing through the heater in amperes and V is the voltage across the coil, then at steady state Q = VI x 10-3 kW.
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Dr. Mandar M. Lele
If m is the mass of steam taken in t seconds under steady flow condition, then the steady flow energy equation for the heater (as control volume) gives w1 h1 +Q = w1h2
Where, w1 = steam flow rate in kg/s
Therefore, h1 +Q/w1 =h2
h1 = hfp1 +x1 hfgp1, hence x1 can be calculated
Electrical Calorimeter